Holt Geometry

11-2 Arcs and Chords

Warm Up

1. What percent of 60 is 18?

2. What number is 44% of 6?

3. Find mWVX.

30

2.64

104.4

Holt Geometry

11-2 Arcs and Chords

Apply properties of arcs.

Apply properties of chords.

Objectives

• A central angle is an angle whose vertex is the center of a circle.

• An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.

Holt Geometry

11-2 Arcs and Chords

Holt Geometry

11-2 Arcs and Chords

Example 1: Data Application

The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.

= 234

mKLF = 360° – mKJF

mKJF = 0.35(360)= 126

mKLF = 360° – 126°

Holt Geometry

11-2 Arcs and Chords

Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST UV.

Holt Geometry

11-2 Arcs and Chords

Example 2: Using the Arc Addition Postulate

mCFD = 180 – (97.4 + 52)= 30.6

= 97.4 + 30.6= 128

mBD = mBC + mCD

mBC = 97.4 Vert. s Thm.

∆ Sum Thm.

mCFD = 30.6Arc Add. Post.

Substitute.Simplify.

Find mBD.

mCD = 30.6

Holt Geometry

11-2 Arcs and Chords

Holt Geometry

11-2 Arcs and Chords

Example 3A: Applying Congruent Angles, Arcs, and Chords

TV WS. Find mWS.

9n – 11 = 7n + 11

2n = 22

n = 11

= 88°

chords have arcs.

Def. of arcs

Substitute the given measures.

Subtract 7n and add 11 to both sides.

Divide both sides by 2.

Substitute 11 for n.

Simplify.

mTV = mWS

mWS = 7(11) + 11

TV WS

Holt Geometry

11-2 Arcs and Chords

Holt Geometry

11-2 Arcs and Chords

Find NP.

Example 4: Using Radii and Chords

Step 2 Use the Pythagorean Theorem.

Step 3 Find NP.

RN = 17 Radii of a are .

SN2 + RS2 = RN2

SN2 + 82 = 172

SN2 = 225SN = 15

NP = 2(15) = 30

Substitute 8 for RS and 17 for RN.Subtract 82 from both sides.Take the square root of both sides.

RM NP , so RM bisects NP.

Step 1 Draw radius RN.

Holt Geometry

11-2 Arcs and Chords

Lesson Quiz: Part I

1. The circle graph shows the types of cuisine available in a city. Find mTRQ.

158.4

Holt Geometry

11-2 Arcs and Chords

Lesson Quiz: Part II

2. NGH 139

Find each measure.

3. HL 21

Holt Geometry

11-2 Arcs and Chords

Lesson Quiz: Part III

12.9

4. T U, and AC = 47.2. Find PL to the nearest tenth.